A364758
G.f. A(x) satisfies A(x) = 1 + x*A(x)^4 / (1 + x*A(x)).
Original entry on oeis.org
1, 1, 3, 14, 76, 450, 2818, 18352, 123028, 843345, 5884227, 41650479, 298352365, 2158751879, 15754446893, 115830820439, 857147952469, 6379136387303, 47715901304501, 358529599468636, 2704884469806606, 20481615947325089, 155605509972859999, 1185779099027494848
Offset: 0
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a(n) = if(n==0, 1, sum(k=0, n-1, (-1)^k*binomial(n, k)*binomial(4*n-3*k, n-1-k))/n);
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a(n, r=1, s=-1, t=4, u=1) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r)); \\ Seiichi Manyama, Dec 11 2024
A364864
G.f. A(x) satisfies A(x) = 1 + x*A(x)^3 / (1 + x*A(x)^3).
Original entry on oeis.org
1, 1, 2, 4, 6, -1, -58, -304, -1090, -2876, -4216, 9244, 106746, 529962, 1874628, 4669760, 4309742, -35179252, -277928680, -1269921008, -4214431912, -9197175241, 30113526, 128659598896, 822227670866, 3453484223084, 10519017940952, 18490932535144
Offset: 0
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a(n) = sum(k=0, n, (-1)^k*2^(n-k)*binomial(n, k)*binomial(3*n+k+1, n)/(3*n+k+1));
A364866
G.f. satisfies A(x) = 1 + x*A(x)^5 / (1 + x*A(x)^5).
Original entry on oeis.org
1, 1, 4, 21, 124, 781, 5120, 34474, 236492, 1644222, 11543644, 81623504, 580104672, 4137414963, 29574658416, 211639869236, 1514729242092, 10832683182538, 77342204972120, 550791674067623, 3908735530965604, 27612614422978557, 193943797650498016
Offset: 0
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a(n) = sum(k=0, n, (-1)^k*2^(n-k)*binomial(n, k)*binomial(5*n+k+1, n)/(5*n+k+1));
A365218
G.f. satisfies A(x) = 1 + x*A(x)^6 / (1 + x*A(x)^6).
Original entry on oeis.org
1, 1, 5, 34, 265, 2232, 19766, 181300, 1706737, 16392049, 159959240, 1581278838, 15800619070, 159321921844, 1618981274136, 16562211506496, 170426473666497, 1762771226922775, 18316562635133813, 191104193378725552, 2001224271292820200
Offset: 0
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a(n) = sum(k=0, n, (-1)^(n-k)*binomial(6*n+1, k)*binomial(n-1, n-k))/(6*n+1);
A365224
G.f. satisfies A(x) = 1 + x*A(x)^4 / (1 + x*A(x)^5).
Original entry on oeis.org
1, 1, 3, 10, 30, 56, -167, -2813, -21515, -126135, -601812, -2179039, -3455504, 32238155, 430944400, 3334419890, 20083350422, 97094186751, 338485665435, 274332822425, -8491831747320, -97735154210032, -732963337489636, -4341176221239330
Offset: 0
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a(n) = sum(k=0, n, (-1)^(n-k)*binomial(5*n-k+1, k)*binomial(n-1, n-k)/(5*n-k+1));
Showing 1-5 of 5 results.
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